Chronological spacetimes without lightlike lines are stably causal

Understand

The statement of the title is proved.

• It implies that under physically reasonable conditions, spacetimes which are free from singularities are necessarily stably causal and hence admit a time function.
• Read as a singularity theorem it states that if there is some form of causality violation on spacetime then either it is the worst possible, namely violation of chronology, or there is a singularity.
• The analogous result: "Non-totally vicious spacetimes without lightlike rays are globally hyperbolic" is also proved, and its physical consequences are explored.